Research in the field of quantum computing began in 1982 when Richard Feynman introduced the concept of a “quantum simulator.” See R. P. Feynman, “Simulating Physics with Computers”, Int. J. Theor. Phys., 21:467–488 (1982). Soon it was determined that a quantum system could be used to yield a potentially exponential time saving in certain types of intensive computations. See D. Deutsch, “Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer”, Proc. of the Roy. Soc. of London A400:97–117 (1985). Since then, research has progressed to include significant software and hardware advances. As the speed of classical computers approaches a projected upper bound due to the natural limits of miniaturization of integrated circuits, so interest in quantum computers has intensified. Indeed many algorithms to run on quantum computers have been written, two notable examples being the Shor and Grover algorithms. See P. Shor, “Polynomial-time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer”, SIAM J. of Comput., 26(5): 1484–1509 (1997), and U.S. Pat. No. 6,317,766 entitled “Fast Quantum Mechanical Algorithms”; and L. Grover, “A Fast Quantum Mechanical Algorithm for Database Search”, Proc. 28th STOC, 212–219 (1996). Nevertheless, sizeable obstacles remain to the development of large-scale quantum computing devices that are both practical and capable of out-performing currently available classical computers. See, for example, “Quantum Dreams”, The Economist, Mar. 10, 2001, pp. 81–82.
In fact, the field of quantum computing remained theoretical until the late 1990's when several hardware proposals were tested. Of these proposals, the most scalable physical systems are those that are superconducting structures. Superconducting material is material that has zero electrical resistance below critical levels of current, magnetic field and temperature. Josephson junctions are examples of such structures that have been of special interest because their observable properties are macroscopic manifestations of underlying quantum mechanical principles.
A preferred physical realization of a quantum computer is based on quantum bits, or “qubits.” Generally speaking, a qubit is a well-defined physical structure that has a plurality of quantum states, that can be isolated from its environment and that can evolve in a quantum mechanical fashion. A survey of the current physical systems from which qubits could be formed can be found in: S. L. Braunstein and H. K. Lo (eds.), Scalable Quantum Computers, Wiley-VCH Verlag GmbH, Berlin (2001), incorporated herein by reference. The information storage and processing capacity of a quantum computer can potentially exceed the capacity of the most powerful classical computers because, according to some views, a quantum computer can be considered to be a parallel machine. In such a view, capacity is considered to be exponential in physical size, nominally measured by the number of qubits, as opposed to the more familiar polynomial relationship between capacity and number of bits for a classical computer. This view of capacity means that as quantum computers grow in size they are destined to substantially outperform the most powerful classical computers that could ever be contemplated.
A series of nominal capabilities are held to be necessary conditions for a physical system to behave as a qubit and for a series of qubits to become a quantum computer. See D. DiVincenzo in Scalable Quantum Computers, S. L. Braunstein and H. K. Lo (eds.), chapter 1, Wiley-VCH Verlag GmbH, Berlin (2001), also published as Los Alamos National Laboratory preprint “quant-ph/0002077” (2000), incorporated herein by reference. These requirements include the need for the system to be scalable, i.e., the ability of the system to combine a reasonable number of qubits. Associated with scalability is the need to eliminate decoherence in a qubit. Also required for a qubit to be useful in quantum computing, is the ability to perform operations that initialize, control and couple qubits. Control of a qubit includes performing single qubit operations as well as operations on two or more qubits. Coupling is an operation performed on two or more qubits. This set of operations also needs to be a universal set, i.e., one which permits quantum computation. Fortunately, many sets of gates are universal, see A. Barenco et al., “Elementary Quantum Gates for Quantum Computation”, Physical Review A 52:3457 (1995), incorporated herein by reference. Finally, it is necessary to be able to measure the state of a qubit in order to perform computing operations.
There are two principal means to realize qubits, corresponding to the limits of well defined charge (charge qubit) or phase (phase qubit). Phase and charge are related variables that, according to basic quantum principles, are canonical conjugates of one another. The division of the two classes of device is outlined in Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-State Engineering with Josephson-Junction Devices”, Reviews of Modern Physics, 73:357 (2001), incorporated herein by reference. Materials that exhibit superconducting properties are attractive candidates for quantum computing applications, since the quantum behavior of the Bose condensates (Cooper pairs) at Josephson junctions have macroscopically observable consequences. Indeed, recently, several designs of a superconducting qubit have been proposed and tested; see Y. Nakamura et al., Nature, 398:786 (1999); J. R. Friedman et al., Nature, 406:43 (2000); C. H. van der Wal et al., Science, 290:773 (2000), all of which are incorporated herein by reference. These qubits have not yet been coupled and controlled in a scalable manner.
The preferred type of superconducting material used depends on the nature of the qubit. Very broadly, the materials are often divided into metals and oxides. However, the ability to deposit metals and oxides (that are not oxides of the deposited metal) on the same chip requires expensive facilities. In general, although it has been found easy to create a layer of metal oxide on the surface of the metal, the metal, it has been difficult to layer copper oxide superconductors in conjunction with other superconducting metals. Further, the conditions, such as extremes of low or high temperature, needed to optimize one process may not be amenable to another. This is a problem because certain types of qubits often require particular materials whereas the corresponding control systems require other types. Thus, implementing qubits is non-trivial.
Furthermore, the nature of qubits is such that their quantum mechanical properties are easily affected by interactions with other systems. Quantum computing requires that qubits be isolated so that the state of a qubit can coherently evolve. However, to permit universal quantum computing, some system with control over, i.e., interaction with, the qubit is needed so that the state of the qubit can be measured, as well as initialized. This apparently contradictory situation arises directly from the quantum behavior of qubits and presents numerous challenges for initialization, control, coupling and measurement of qubits. Accordingly, now that scalable quantum computing is becoming less of a theoretical dream and more of a physical reality, ways of devising and implementing solutions to the hardest technical challenges are being investigated. In particular, systems in which qubits can be controlled and measured in ways that do not perturb their internal quantum states are being sought. The implementation of multiple qubits in a single device, and in a controllable manner, so that qubits may couple with one another thereby permitting classical logic operations to be performed, is central to the goal of building a quantum computer. Hitherto, previous methods of coupling model qubits in quantum computing devices have been unwieldy, being based on optics (entanglement of photons) or nuclear magnetic resonance (utilizing spin states of atoms and molecules).
Recently inductive coupling between phase qubits has been described in: T. P. Orlando, J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd, and J. J. Mazo, “Superconducting Persistent Current Qubit”, Phys. Rev. B 60:15398 (1999), and Y. Makhlin, G. Schön, and A. Shnirman, “Quantum-State Engineering with Josephson-Junction Devices”, Reviews of Modem Physics 73:357 (2001), at page 369, each of which is incorporated herein by reference. These qubits have also not yet been coupled and controlled in a scalable manner, however.
Inductive coupling with qubits for the purpose of readout has also been investigated. See, e.g., T. P. Orlando, Lin Tian, D. S. Crankshaw, S. Lloyd, C. H. van der Wal, J. E. Mooij, and F. Wilhelm, “Engineering the Quantum Measurement Process For The Persistent Current Qubit” Physica C 368:294–299 (2002), and H. Tanaka, Y. Sekine, S. Saito and H. Takayanagi, “DC-SQUID Readout For Qubit,” Physica C 368:300–304 (2002), each of which is incorporated herein by reference in its entirety. Measurement and characterization of these quantum devices relied on a DC SQUID (Superconducting QUantum Interference Device). The experiments of Orlando et al., couple a DC-SQUID inductively to a flux qubit, where the qubit includes a superconducting loop and three Josephson junctions. Both the DC-SQUID and flux qubit are fabricated on the same substrate. The use of such a SQUID for testing and characterization may have drawbacks, including decohering the system through a strong back action, or the necessity of taking many measurements. Inference from data acquired in this manner requires a large number of measurements from which the device characteristics can be statistically inferred and data takes months to collect.
Therefore, a more immediate and unintrusive method for measurement and characterization of qubits is needed, and one that permits scalable coupling between qubits and other circuitry.